Cronulla’s Paul Gallen is one of the players who pondered the deal on Friday morning. Photograph: Mark Metcalfe/Getty Images

Most past and present Cronulla NRL players implicated in the Asada scandal have elected to accept a deal under which they may miss just three matches, reports say.

Skipper Paul Gallen is believed to be among 10 current NRL players to have accepted bans from the Australian Sports Anti-Doping Authority (Asada) on Friday over their involvement in the supplements program at the club in 2011.

The agreement offers them a 12-month ban, backdated to November 2013.

Players still with Cronulla would miss only three games, but others who have since moved to other clubs, such as the North Queensland centre Matthew Wright, would potentially also be rubbed out for this year’s finals.

It was unconfirmed which players had agreed to accept the deal, though Newcastle coach Wayne Bennett said Knights players Jeremy Smith and Kade Snowden were among them.

“Under the terms of reference they have deemed to have served a period of time, and have been given a three-month suspension and will be available some time in November ... they have to accept the situation, the reality of it all.

“Of course it was a difficult choice ... I have no understanding of the other 15 players involved, it was when they were at Cronulla in 2011.”

English Super League players Paul Aiton and Ben Pomeroy are said to have rejected the bans.

The players had until Friday morning to accept the offer. They reportedly received assurances from the World Anti-Doping Agency that the international body would not appeal against the terms agreed between Asada and the players.

Their admissions are likely to be used as evidence against support staff.

NRL boss David Smith said he hoped the 18-month investigation was finally reaching a conclusion.

“I’m not completely up to date, as to who has decided to do what, but I do know that process is going on in the background for all the players that were issued with show cause [notices],” Smith told Channel Nine.

“If we can bring the thing to an end, if we can get the right response whereby the punishment fits the crime, whereby anybody that is involved with the game that has had a duty of care is not involved in our game any more and we can finally put this behind us then the right things have taken place in the right way, and I think we have managed the process pretty well so far.

“Then of course we will all be happy and the fans will be happy and the game can move on and we have some clear blue air next season.”

The NRL released a statement on Friday afternoon confirming players involved in the Asada investigation had responded to the show-cause notices.

“The NRL’s process will not begin until such time as we receive formal notification from Asada based on player responses to the show-cause notices,” the statement said.

Meanwhile the AFL boss Gillon McLachlan and Asada have denied Fairfax Media reports that Asada offered Essendon players a reduced sanction if they accepted they took performance-enhancing substances in 2011-12.

The deal would have to come before a ruling in the federal court case brought by Essendon challenging the legality of the AFL/Asada investigation, the report said.

McLachlan said he was not aware of any such offer and had spoken to his Asada counterpart Ben McDevitt on Friday morning to confirm nothing had been tabled.

“I rang Ben to make sure that I hadn’t somehow missed something or got that wrong,” he told Fairfax Radio in Melbourne on Friday.

“He said categorically ‘no’.”

Asada later backed McLachlan’s view.

“At no time has Asada put forward a sanction proposal to Essendon players, or their legal representatives, linked to the timing of the federal court decision,” it said in a statement on Friday.

“Asada can also confirm that it has not ‘tabled’ a sanction proposal with the AFL chief executive regarding Essendon football players.”

McLachlan said McDevitt indicated earlier this year, after players were issued show-cause notices, that the Asada Act had provisions to reduce sanctions for “substantial assistance” or “no significant fault”.

“So I think that six-month thing has been around and broadly well-known, but I haven’t had a deal put on my desk,” he said.

Asked whether there was an existing offer on the table to the Bombers players for reduced sanctions, McLachlan replied: “I don’t know specifically and I don’t want to comment beyond that.”

He admitted the situation had been complicated by the reduced and backdated bans offered to Cronulla players because of the “inordinate delay” in Asada’s investigation.

“If it’s true what ... the offer to the Cronulla players is, that the [ban] gets backdated, it may be that they serve a minimum of three months,” he said.

With the federal court yet to hand down its decision on the legality of the AFL and Asada’s joint investigation into Essendon’s supplements program, McLachlan said everything else had essentially been “frozen”.

But he hoped things would be resolved in time for next season.

“I certainly hope that we go into 2015 with resolution and clarity,” he said.